A new serial approach of the forward kinematic model of spherical parallel manipulators for real

Parallel architectures are increasingly used as haptic devices to provide low inertia, high stiffness and compactness. Thus, spherical parallel manipulators have been developed to generate the three rotational movements in a sufficient workspace. However, these parallel structures have complex kinematic models and can suffer from critical singularity issues. This paper proposes a serial approach to solve the forward kinematic model of a spherical parallel manipulator, which is used as a haptic device in minimally invasive surgery. The new forward kinematic model is based on the serial positioning of the three sensors on one leg rather than placing the three sensors on the three actuated base joints. The forward kinematic model calculation is thus simplified to be suitable for real-time applications (computing time around 5？μs) without cost increase. Parallel singularity effects are removed using this approach and the accuracy of the forward kinematic model is highly enhanced. Simulations were carried out to show the benefits of this approach. The resulting errors of the forward kinematic model calculation due to measurement noises do not exceed 0.2° along the workspace. Experiments were carried out to demonstrate the control of a surgical robot